Unformatted text preview: T > t} = P {T1 > t and T2 > t} = P {T1 > t}P {T2 > t} = e 0 −h1 (s)ds e Rt
0 −h2 (s)ds = e− Rt
0 h(s)ds where h = h1 + h2 . Therefore, the failure rate function for the minimum of two independent random
variables is the sum of their failure rate functions. This makes intuitive sense; if there is a system
that fails when either of one of two components fails, then the rate of system failure is the sum of
the rates of component failure. 3.10. BINARY HYPOTHESIS TESTING WITH CONTINUOUSTYPE OBSERVATIONS
(a) h(t) (b) 113 h(t) t t Figure 3.24: Failure rate functions for (a) nearly constant lifetime and (b) an item with a burnin
period (bath tub failure rate function) Two commonly appearing types of failure rate functions are shown in Figure 3.24. The failure
rate function in Figure 3.24(a) corresponds to the lifetime T being nearly deterministic, because
the failure rate is very small until some ﬁxed time, and then it shoots up quickly at that time; with
high probability, T is nearly equal to the time at which the failur...
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 Spring '08
 Zahrn
 The Land

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